To understand the hydrodynamization of the QGP, one needs to follow its evolution from the earliest stages, where a perturbative description in the forms of the glasma effective theory [1]} and subsequently kinetic theory [2]}, [3]} is applicable, to later epochs when the soft gluons form a strongly coupled thermal bath. The semi-holographic framework, briefly reviewed in Sec. , allows for simple phenomenological constructions where the evolution of both perturbative (weakly self-interacting) and non-perturbative (strongly self-interacting) degrees of freedom can be described simultaneously in a consistent way [4]}, [5]}, [6]}, [7]}, [8]}, [9]}, [10]}. In the simplest model, one retains only two effective metric couplings, and reduces both sectors to viscous fluids each following the Müller-Israel-Stewart (MIS) [11]}, [12]} description with different amounts of viscosities. The effective metric couplings permit the exchange of energy and momentum, while the total energy-momentum tensor, which can be constructed readily from the subsector energy-momentum tensors, is conserved in the physical background (Minkowski) metric. For further simplicity, the fluids describing both sectors are assumed to be conformal. The full system deviates from conformality, however, since the effective metric couplings (denoted by \(\gamma \) , \(\tilde{\gamma }=r\gamma \) ) have mass dimension \(-4\) . We assume them to be given in terms of a saturation scale that sets the scale for the energy densities of the QGP when perturbative descriptions tend to break down.At this point, we note that although we are calling the full non-perturbative description semi-holographic, we are only using an effective fluid description for the strongly coupled non-perturbative sector with the expectation that our simplification should be sufficient to learn about hydrodynamization. The explicit dual holographic description will be necessary to understand the role of irreversible energy transfer to a dynamical black hole which is expected to be a slow process determined by the coupling between the two sectors based on results obtained in [10]}.
